I have had my betta for about 3 months now, but just did a recent tank change because I lost my other betta which was in a larger tank. I cleaned all the parts to the larger tank thoroughly as well as the pebbles and accessories. I replaced all the water and balanced the pH appropriately as well as installed a new heater I just bought before putting him into the new tank. My betta has been in this new tank for about 8 hours and he is swimming very erratically and is unable to stay down in the tank very well (he sems to be involuntarrily floating to the top). My previous betta had swim bladder and was acting similarly to this, but I was unable to save him from it. Is there anything I can do to prevent losing another betta to this disease? I have tried giving him bioled, shelled peas, but he is either unable or unwilling to eat them. Any advice?

Dont give him peas! Bettas are carnivores and actually cant digest peas very well. Try epsom salts you can get them at any drug store. Most swim bladder can be cured by fasting for a few days, but my rescue had to have epsom salts it was really bad! Just add 1 tEaspoon per gallon. And do water changes daily. It took my rescue 3 days to get over it, but urs shouldnt take that long, also try frozen daphnia that u can find at a petstore. If a few days have passed and hes still like it try going to 2 teaspoons. Then if it still doesnt work go to three. Dont go past 10 days though with the treatment, once hes cured stop treatment and do a 100% water change

SBD, as far as I understand, isn't contagious.....its caused generally by poor nutrition and over feeding.

Definitely best to avoid the pea treatment, as Gracie said.....bettas are carnivorous fish, they don't digest plant/vegetable matter very well and the pea treatment, while a few have had success, generally can just cause more digestive issues.
Frozen(NOT freeze-dried)Daphnia is a good betta-safe substitute for the pea treatment.

What sort of food are you regularly feeding your fish, how often, and how much? What is the temp of the tank? Does he appear bloated as well?